Cogwheel

Intro

Create a Cogwheel (AKA Cog or Gear) primitive as part of a Basic Shape.

UI

Teeth - Set the number of teeth or cogs.

Pitch Radius - Set the radius from the centre to the midpoint of each tooth.

Hole Radius - Set the radius of the hole.

Tooth Depth - Set a value for the total height of each tooth.

Tooth Width - Set the width of each tooth at its midpoint.

Tooth Taper - Set the inner and outer taper angles for each tooth.

Midpoint Position - Set the midpoint of each tooth where 0 is the base of the tooth and 1 is the tip.

Gear Example

All rotation is driven by the medium Cogwheel.

In order to create a gear system there are some basic guides to follow:

• The Module of each Cogwheel must match. The module is a ratio which can be easily expressed as: $Module = 2 * Pitch Radius / Number Of Teeth$
• The teeth must be the same shape/size.
• The Pitch Circle of each Cogwheel must be 'touching'.

In the example below:

• the Medium Cogwheel has a Pitch Radius of 200 and 12 Teeth.
• the Small Cogwheel has a Pitch Radius of 100 and 6 Teeth.
• the Large Cogwheel has a Pitch Radius of 400 and 24 Teeth.

200 / 12, 100 / 6 and 400 / 24 all equal 16.66 so each Cogwheel has the same Module.

The math for the rotation is also quite simple. If:

• r1 = Rotation of the Medium Cogwheel
• t1 = Number of Teeth of the Medium Cogwheel
• r2 = Rotation of the Small Cogwheel
• t2 = Number of Teeth of the Small Cogwheel

$r2 = r1 * t1 / t2$

In the case of Medium > Small that would be:

$r2 = r1 * 12/6$

A Jsmath Utility can be used to rig this equation up.

1. Create a Jsmath Utility.
2. Add the expression -n0 * n1/n2
3. Add 3 indices.
4. Connect Medium.rotation→jsmath.index0
5. Connect Medium.teeth→jsmath.index1
6. Connect Small.teeth→jsmath.index2
7. Connect jsmath.id→Small.rotation

As he Medium Cogwheel rotates, the Small Cogwheel will rotate at the correct speed so they both mesh with each other. In order to position them correctly, move them 300 apart in X (the total of their Pitch Radius values).